A general schematic diagram of a photolithography system is shown in FIG. 1. Energy from an illumination source 100 is passed through a mask 110 and focused onto a photo-sensitive surface 120. The mask contains patterned regions, such as regions 130, 131, 132. The goal of the photolithography system is generally to reproduce the pattern on the mask 110 on the photo-sensitive surface 120. One or more optical components—such as lenses 140 and 142—may be used to focus and otherwise manipulate the energy from the illumination source 100 through the mask 110 and onto the surface 120. The resulting image on the photo-sensitive surface allows the surface 120, and ultimately underlying layers, to be patterned. Photolithography is widely used in typical semiconductor processing facilities to create intricate features on various layers forming integrated circuits or other micromachined structures.
As the feature sizes desired for reproduction on the photosensitive surface shrink, it is increasingly challenging to accurately reproduce a desired pattern on the surface. Numerous optical challenges are presented, including those posed by diffraction and other optical effects or process variations as light is passed from an illumination source, through a system of lenses and the mask to finally illuminate the surface.
Optical proximity correction tools, such as Progen marketed by Synopsys, are available to assist in developing mask patterns that will reflect optical non-idealities and better reproduce a desired feature on a desired surface. For example, “dog-ears” or “hammer head” shapes may be added to the end of linewidth patterns on the mask to ensure the line is reproduced on the surface completely, without shrinking at either end or rounding off relative to the desired form.
For example, FIG. 2 depicts an initial mask pattern 200 designed to reproduce rectangle 201. The actual feature reproduced on surface 230, after the lithography, may look something like feature 220, considerably shorter and rounder than the desired rectangle 201. An optical proximity correction system, however, could generate a modified mask pattern 250. The modified pattern 250 yields, after lithography, the feature 260, considerably closer to the initial desired feature 201.
Optical proximity correction tools, used to generate the modified mask pattern 250, for example, generate models of the intensity profile at the photo-sensitive surface after illumination of a mask with an illumination source. Intensity is typically represented by a scalar value. The intensity at a surface illuminated through a mask in a lithography system can be calculated generally by taking the convolution of a function representing the mask with a set of functions representing the lithography system that includes the illumination source. The set of functions representing the lithography system are eigenfunctions of a matrix operator.
Hopkins imaging theory provides the rigorous mathematical foundation for intensity calculations. The theory provides that intensity, in the spatial domain, is given by:I(x,y)=∫∫∫∫J(x1−x2,y1−y2)O*(x1,y1)O*(x2,y2)H(x−x1,y−y1)H*(x−x2,y−y2)dx1dx2dy1dy2 where x and y are coordinates in the spatial domain. O represents a mask pattern, H is a lens pupil function and J is a source pupil intensity function. A Fourier transform yields intensity in the frequency domain, given by:I(x,y)=∫∫∫∫∫∫J(f·g)H(f+f1,g+g1)H*(f+f2,g+g2)O*(f1,g1)O*(f2,g2)e−i2π[(f1−f2)x+(g1−g2)y]dfdgdf1dg1df2dg2 where f and g are coordinates in the frequency domain. As described further below, the frequency domain is also representative of the pupil plane in an illumination system.
This comprehensive theory provides for calculations of a complete intensity profile. To be useful, however, an optical proximity correction tool should generate an intensity profile within a reasonable amount of time to practically alter the mask design. Accordingly, the optical proximity correction tools make various simplifications and approximations of actual optical effects. In particular, optical proximity correction tools generally do not take into account polarization of an illumination source, or variation of that polarization across the illumination pupil.
The polarization of an electromagnetic wave is generally the angle of oscillation. For example, in FIG. 3, wave 310 is shown propagating in direction 300. The oscillations, however, may occur at any angle perpendicular to the direction of propagation, shown by circle 320. The polarization angle of energy emitted by an illumination source may alter the diffraction effects experienced by the energy, and therefore ultimately, the pattern generated at the photo-sensitive surface.